Ug1ddlZddlZddlZddlZddlmZddlmZddl m cm Z ddl mZddlmZdgZdZGd dZe jfd Zde jd d ZdS)N)prod)_bspl) csr_array) _not_a_knot NdBSplinecptj|tjr tjStjS)z>Return np.complex128 for complex dtypes, np.float64 otherwise.)np issubdtypecomplexfloating complex128float64dtypes [/var/www/surfInsights/venv3-11/lib/python3.11/site-packages/scipy/interpolate/_ndbspline.py _get_dtypers) }UB.//}zcDeZdZdZdddZddddZed dZdS) raTensor product spline object. The value at point ``xp = (x1, x2, ..., xN)`` is evaluated as a linear combination of products of one-dimensional b-splines in each of the ``N`` dimensions:: c[i1, i2, ..., iN] * B(x1; i1, t1) * B(x2; i2, t2) * ... * B(xN; iN, tN) Here ``B(x; i, t)`` is the ``i``-th b-spline defined by the knot vector ``t`` evaluated at ``x``. Parameters ---------- t : tuple of 1D ndarrays knot vectors in directions 1, 2, ... N, ``len(t[i]) == n[i] + k + 1`` c : ndarray, shape (n1, n2, ..., nN, ...) b-spline coefficients k : int or length-d tuple of integers spline degrees. A single integer is interpreted as having this degree for all dimensions. extrapolate : bool, optional Whether to extrapolate out-of-bounds inputs, or return `nan`. Default is to extrapolate. Attributes ---------- t : tuple of ndarrays Knots vectors. c : ndarray Coefficients of the tensor-produce spline. k : tuple of integers Degrees for each dimension. extrapolate : bool, optional Whether to extrapolate or return nans for out-of-bounds inputs. Defaults to true. Methods ------- __call__ design_matrix See Also -------- BSpline : a one-dimensional B-spline object NdPPoly : an N-dimensional piecewise tensor product polynomial N) extrapolatect|} t|n#t$r |f|z}YnwxYwt||kr0tdt|dt|dtd|D|_td|D|_t j||_|d}t||_ t j||_t|D]}|j|}|j|}|j d|z dz } |dkrtd |d |j dkrtd |d | |dzkrtd d|zdzd|d|dt j|dkrtd|dtt j||| dzdkrtd|dt j|std|d|jj |krtd|d|jj || krK|]}tj|VdSN)operatorindex).0kis r z%NdBSpline.__init__..Ys,66bx~b))666666rc3LK|]}tj|tV dSrN)r ascontiguousarrayfloatrtis rrz%NdBSpline.__init__..Zs2IIr+Be<<<IIIIIIrTrrzSpline degree in dimension z cannot be negative.zKnot vector in dimension z must be one-dimensional.zNeed at least z knots for degree z in dimension zKnots in dimension z# must be in a non-decreasing order.z.Need at least two internal knots in dimension z should not have nans or infs.zCoefficients must be at least z -dimensional.z,Knots, coefficients and degree in dimension z are inconsistent: got z coefficients for z knots, need at least z for k=r)len TypeError ValueErrortuplektr asarraycboolrrangeshapendimdiffanyuniqueisfiniteallrrr!) selfr+r-r*rr1dtdkdndts r__init__zNdBSpline.__init__Ms1vv  FFFF   T AAA  q66T>>;A;;s1vv;;;<< <66A66666IIqIIIIIA  K ,,At - -ABB b 1$AAvv "/q"/"/"/000w!|| "6Q"6"6"677726zz "z&NdBSpline.__call__..s***RR***rc3 K|] }|dzV dS)rNrC)rr:s rrz%NdBSpline.__call__..s&..b1f......r)r@c.g|]}|jjzSrC)ritemsize)rsc1s rrEz&NdBSpline.__call__..s3"7"7"7&'#$rx'8"8"7"7"7r)!r&r+rr.r zerosintcr,r1r0r(r3r"reshaper!r*remptymaxfillnanr/r) unravel_indexarangerintpTr-ravelstridesrevaluate_ndbspline)r7xir>rr1xi_shape_klen_t_tr8r0indices _indices_k1dc1r _strides_c1num_c_troutrJs @r__call__zNdBSpline.__call__s*46{{  *K;'' :4'111BBBbg...Bw!||rx{d22 -2--!$&kk---...26{{ O !Mb!M!MNNNZ% ( ( (8 ZZHRL ) )  !" % % B<4  KKKTKKLL LZbhv&6&6 7 7 7+*46*** XtSZZ( 6 6 6 t / /A%)VAYBq/3tvay>>/! " " 5(8(8999..tv....."29T%[[#9#95AAz'999; V^^DFL$/%7 8 8hhjjj"7"7"7"7+-:"7"7"7>@gGGG 8B<hrx}{2"(CCC  !#!&!#!#!,!$!)!,!-!$ ' ' '{{8CRC=46<+>>???rTctj|t}|jd}t ||kr#t dt |d|d t |n#t $r |f|z}YnwxYwtj|tj}tj |||\}}} t||| fS)a Construct the design matrix as a CSR format sparse array. Parameters ---------- xvals : ndarray, shape(npts, ndim) Data points. ``xvals[j, :]`` gives the ``j``-th data point as an ``ndim``-dimensional array. t : tuple of 1D ndarrays, length-ndim Knot vectors in directions 1, 2, ... ndim, k : int B-spline degree. extrapolate : bool, optional Whether to extrapolate out-of-bounds values of raise a `ValueError` Returns ------- design_matrix : a CSR array Each row of the design matrix corresponds to a value in `xvals` and contains values of b-spline basis elements which are non-zero at this value. rr@z*Data and knots are inconsistent: len(t) = z for ndim = r) r r,r"r0r&r(r'int32r _colloc_ndr) clsxvalsr+r*rr1kkdatar^indptrs r design_matrixzNdBSpline.design_matrixs0 5...{2 q66T>>SVV   FFFF   T AAA Z * * * % 02 > >gv$0111s A00BB)T)__name__ __module__ __qualname____doc__r=rd classmethodrmrCrrrrs11d047878787878r"&4V@V@V@V@V@p&2&2&2[&2&2&2rc tj|jtjr0t ||j|fi|}t ||j|fi|}|d|zzS|jdkr|jddkrptj |}t|jdD]?}|||dd|ffi|\|dd|f<}|dkrtd|d|d|d@|S|||fi|\}}|dkrtd|d |d|S) Ny?r%rrz solver = z returns info =z for column rz returns info = ) r r rr _iter_solverealimagr1r0 empty_liker/r() absolver solver_argsrurvresjinfos rrtrtsg  }QWb0111aff<< <<1aff<< <<bg~v{{qwqzA~~mAqwqz"" R RA$fQ!!!Q$??;??OC1Itqyy !PF!P!P!P!PA!P!P!PQQQ F1a//;// T 199>>>D>>>?? ? rrzc t}tdD} tn#t$r f|zYnwxYwtD]]\}}tt j|} | |kr+t d| d|d|d|dzd ^tfdt|D} t jd tj Dt } t | | } |j} t| d |t| |d f}||}|t"jkr$t'jt*| }d |vrd|d <|| |fi|}||| |d z}t| |S)aConstruct an interpolating NdBspline. Parameters ---------- points : tuple of ndarrays of float, with shapes (m1,), ... (mN,) The points defining the regular grid in N dimensions. The points in each dimension (i.e. every element of the `points` tuple) must be strictly ascending or descending. values : ndarray of float, shape (m1, ..., mN, ...) The data on the regular grid in n dimensions. k : int, optional The spline degree. Must be odd. Default is cubic, k=3 solver : a `scipy.sparse.linalg` solver (iterative or direct), optional. An iterative solver from `scipy.sparse.linalg` or a direct one, `sparse.sparse.linalg.spsolve`. Used to solve the sparse linear system ``design_matrix @ coefficients = rhs`` for the coefficients. Default is `scipy.sparse.linalg.gcrotmk` solver_args : dict, optional Additional arguments for the solver. The call signature is ``solver(csr_array, rhs_vector, **solver_args)`` Returns ------- spl : NdBSpline object Notes ----- Boundary conditions are not-a-knot in all dimensions. c34K|]}t|VdSrrD)rxs rrzmake_ndbspl..@s(,,SVV,,,,,,rz There are z points in dimension z , but order z requires at least rz points per dimension.c3K|]9}ttj|t|V:dSr )rr r,r")rr8r*pointss rrzmake_ndbspl..OsX$$"*VAYe<<.Qs@@@r@@@rrNratolgư>)r&r)r' enumerater atleast_1dr(r/r, itertoolsproductr"rrmr0rrMsslspsolve functoolspartialrt)rvaluesr*rzr{r1rZr8pointnumptsr+rimatrv_shape vals_shapevalscoefs` ` r make_ndbsplr sb> v;;D,,V,,,,,H A  DIf%%AA5R]5))** QqT>>@&@@q@@+,Q4@@!"1a@@@AA A  $$$$$T{{$$$ $ $A J@@Y%6%?@@@ N N NE  " "5!Q / /D lGwuu~&&WTUU^(<(<=J >>* % %D ";v>>>  $ $"&K  6$ , , , ,D <<7455>1 2 2D Qa  s<AA)r)rrrnumpyr mathrrscipy.sparse.linalgsparselinalgr scipy.sparser _bsplinesr__all__rrgcrotmkrtrrCrrrs+!!!!!!!!!"""""""""""" -k2k2k2k2k2k2k2k2\![0E!s{E!E!E!E!E!E!E!r